FIG. 1 shows a diagram of a conventional localization system based on the pattern-matching algorithm, which is disclosed in “RADAR An In-Building RF-based User Location and Tracking System”, by P. Bahl and V. N. Padmanabhan from pages 775-784, IEEE INFOCOM at 2000s. The positioning system using RADAR includes two phases, which are a training phase and a positioning phase.
In the training phase of the aforesaid RADAR location and tracking system, a plurality of training locations ={, . . . , } are specified as their coordinates in a Cartesian coordinate system defining a training area are given and thus known, which are λ1=<x1,y1>, λ2=<x2,y2>, λ3=<x3,y3>, . . . , λm=<xm,ym>. It is noted that there can be a plurality of beacons, i.e. B={b1, . . . , bn}, located in the neighborhood of each training location for enabling the signals emitted from those neighboring beacons to be receivable by such training location so that a sample containing signal strength information for that specific training location can be formed regarding to those neighboring beacons. Thereby, there can be a plurality of samples being formed in correspondence to the plural training locations in a manner that the feature vector vi=[vi,1, vi,2, . . . , vi,n] of each training location can be established, wherein vi,j, j=1 . . . n is the average signal strength of the beacon bj for the training location λ1. Consequently, all those established feature vectors along with their paired training locations are registered and thus form a database.
In the positioning phase, the object to be positioned is configured with a wireless receiver for enabling the same to receive signals from its neighboring beacons in a real time manner. Accordingly, the received signal strengths (RSS) are used to form a signal strength fingerprint, i.e. s=[s1, s2, . . . , sn], which is then compared with those information stored in the aforesaid database for finding a training location with the most similar feature vector and thereby locating the position of the object. Operationally, the system defined the differences between the real-time signal strength fingerprint of the object with those feature vectors as a function h, and thus the comparison performed for positioning the object can be represented by a discrete function h: →R+. Consequently, the object is to find a training location that can minimize the value of the function h. For instance, when the similarity function h is defined as the Euclidean Distance between two vectors, and there are three training locations λ1, λ2, λ3 and two beacons being located in a test signal space, the three Euclidean Distances between the three training locations and a test object can be computed and thereafter the position of the one training location with the minimum Euclidean Distance is selected to be the location of the test object.